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We propose a thin and compact concentrator photovoltaic (CPV) module, about 20 mm thick, one tenth thinner than those of conventional CPVs that are widely deployed for mega-solar systems, to broaden CPV application scenarios. We achieved an energy conversion efficiency of 37.1% at a module temperature of 25 °C under sunlight irradiation optimized for our module. Our CPV module has a lens array consisting of 10 mm-square unit lenses and micro solar cells that are directly attached to the lens array, to reduce the focal length of the concentrator and to reduce optical losses due to reflection. The optical loss of the lens in our module is about 9.0%, which is lower than that of conventional CPV modules with secondary optics. This low optical loss enables our CPV module to achieve a high energy conversion efficiency.
© 2015 Optical Society of America
1. Introduction
Concentrator photovoltaics (CPVs) convert solar energy into electric power by concentrating sunlight through lenses onto III-V semiconductor-based solar cells with an energy conversion efficiency that can exceed 40% [1]. In CPV modules, the area of the solar cells themselves can be reduced to only 0.1 - 0.2% of the total module area: all the remaining area is occupied by low-cost plastic lenses. This structural feature enables CPVs to achieve higher energy conversion efficiency at lower cost than other photovoltaics. Conventional CPVs that are in wide use for mega-solar system have large lenses to concentrate the sunlight and heat sinks to disperse the heat absorbed by the solar cells, with the result that the modules are thicker and heavier than those of flat-type photovoltaics. CPVs with bulky and heavy structures are not suitable for deployment in cramped spaces in urban areas, since they needs more powerful heavy machinery for installation than do flat photovoltaic panels, increasing the ratio of installation cost to system cost. Thin and compact CPV modules have potential for installation in restricted spaces, such as along roads, in parks, or on rooftops at low cost comparable to flat photovoltaic panels, broadening the potential range of their application scenarios.
CPV modules with micro solar cells and compact lens arrays that achieve high conversion efficiency are increasingly available. Sheng et al. have proposed a compact CPV module about 6 cm thick, in which a secondary ball lens is placed on the active area of each individual solar cell, which measures 0.6 mm x 0.6 mm [1]. Yoon et al. proposed a concentrator module with micro-lenses that have a focal length of about 2.2 mm that are placed on thin-film Si solar cells [2]. Price et al. proposed a CPV module in which a GaAs microcell measuring 0.7 mm x 0.7 mm is sandwiched by an upper refractive lens and a lower reflective lens with focal lengths of f = 15 mm and f = 30 mm, respectively [3].
We have proposed a CPV module that is about 20 mm thick. The module is assembled by placement of the solar cells directly on the back side of the lens array using a self-alignment mechanism, without the use of secondary optics, and attachment of a circuit board on the back side of the lens array. In addition to the advantages of having a thin and compact structure, the use of small solar cells delivers better photovoltaic performance than seen with conventional CPVs. Highly efficient heat dispersion from the solar cell keeps it cool, and, since the cells are placed directly on the lens array, there is no air gap between the top face of the lens and the top face of the solar cell to cause optical losses. We assembled a CPV module measuring 5 cm x 5 cm and achieved an energy conversion efficiency of 34.7% with one solar cell in the module under sunlight [4–6].
In our recent investigations into the effects of sunlight intensity distribution in the solar cell on the photovoltaic characteristics of our modules, we found that the influence of non-uniform irradiation in the 3-junction cells of the triple-junction solar cell on fill factor (FF) and the conversion efficiency to be small. In contrast, the irradiated area of sunlight absorbed by the top cell of the triple-junction solar cell has a greater effect on FF, and therefore energy conversion efficiency, than does any non-uniformity of sunlight caused by chromatic and comatic aberration [7]. This is not the case with conventional CPV modules that have solar cells with side lengths greater than several millimeters: the larger the irradiation area of sunlight in the top cell, greater the FF value. The photo-carriers generated in the top cell flow laterally into the grid electrodes on the top cell. Since the sheet resistance of the top cell is chiefly responsible for the series resistance of our solar cell, a large irradiation area in the top cell decreases photocurrent density and thus suppresses Joule loss caused by sheet resistance of the top cell. The result is an increase in FF value.
It is important to seek the maximum energy conversion efficiency for our module structure under optimal conditions in our measurements of the module to achieve the best performance, since the maximum efficiency is the ultimate target of the CPV system we are developing. This report describes our module, in which the irradiated area of sunlight absorbed at the top cell is optimized from our previous study [7]. We measured its photovoltaic characteristics under various direct normal irradiance (DNI) and sunlight spectra to find the maximum energy conversion efficiency. We demonstrate that our CPV module achieves an energy conversion efficiency of 37.1% under optimal conditions and analyze the energy loss in our CPV module structure.
2. Experimental method
2.1 Module structure
Figures 1(a) and 1(b) are, respectively, a photograph and a schematic cross-sectional diagram of the CPV module used in this report. Solar cells were grown by molecular-beam epitaxy [6]. The module measures 50 by 50 by 19 mm, and is composed of a lens array and a circuit board on which the solar cells are fixed using transparent silicone resin with no air gap [Fig. 1(b)]. The lens array is made of polymethyl methacrylate (PMMA) and a glass plate. It has 25 discrete lenses, each with a 10 mm x 10 mm aperture and is 8.5 mm thick. The top surface of the lens is covered with an anti-reflective coating. The circuit board is composed of an aluminum plate whose front side is covered with an insulation film with wiring patterns formed on the insulating film. The circuit board was wired to allow each solar cell to be measured individually. The 25 solar cells were not interconnected.
Fig. 1 (a) Photograph of a CPV module, (b) schematic cross-sectional image of the CPV module structure, (c) optical microscope image of the solar cell, and (d) schematic cross-section image of the solar cell along line A-A in (c).
Figures 1(c) and 1(d) show an optical microscope image and a schematic sectional image of the solar cell. The solar cell measures 0.97 x 0.97 x 0.2 mm, and has a 0.672 mm2 octahedral photovoltaic region (aperture area). A positive and a negative pad electrode are formed around the solar cell [Fig. 1(c)]. The solar cells are electrically connected to the circuit board by wire bonding. In the photovoltaic region, a lower contact layer, pn-junctions of GaInNAsSb, the GaAs, the InGaP, and an upper contact layer are stacked on a semi-insulating GaAs substrate. The grid electrode and anti-refractive coating are formed on the solar cell’s top face [Fig. 1(d)]. The pattern of the grid electrode is 4 μm in width and 94 μm in pitch. The modules used in this report were assembled using solar cells that had been fabricated on the same wafer to ensure that each module had the same photovoltaic characteristics.
Figure 2 shows the sunlight distribution in the solar cell of the module. The top, middle and bottom cells absorb sunlight a wavelengths of 400 - 665 nm, 665 - 885 nm and 885 - 1350 nm, respectively [Fig. 2(a)]. The thickness of the lens array was designed such that the irradiated area of sunlight absorbed by the top cell is as large as possible to decrease Joule loss caused by sheet resistance in the top cell. The side of the top cell is about 0.6 mm, larger than that of the middle and the bottom cell [Fig. 2(b)]. The glass plate is 10.25 mm thick. The distance from the top of the lens to the surface of the solar cell is 19.05 mm. The concentration ratio of lens area to aperture area of the cell is 150 SUN.
Fig. 2 (a) Schematic cross-sectional images of a lens to which a solar cell is attached. In the upper Figure, the blue, yellow, and red lines indicate 400, 665, and 885 nm-wavelength light. In the lower Figure, the blue, yellow, and red regions correspond to regions irradiated with 400 - 665, 665 - 885, and 885 - 1300 nm wavelength light. Arrows show photocurrent flows. (b) The sunlight intensity distribution on the aperture area of the solar cell calculated by ZEMAX (optical simulation software) by ray tracing. In this simulation, the angular distribution of the incident light was uniform in the range of ± 0.25° in consideration of the behavior of sunlight. Red lines show the position of the grid electrode. Each intensity distribution map measures 1.0 mm x 1.0 mm.
The structure of the CPV module used in this report is not the same as that reported previously [4–7]. However, both have the same fundamental structure: the micro-sized solar cells are attached to the back of the lens array without secondary optics, giving, we assume, the same photovoltaic characteristics using the CPV module in Fig. 1 as those previously reported. The solar cell used in this report has a simple structure, thus we avoid the risk of obtaining unpredicted variations in photovoltaic (PV) characteristics caused by process variations of the cells or electric contact failures. This report’s module is suitable to seek the best performance of our module structure, so in this study, we do not take the cost of the module into account. The concentration ratio of the module in this study is 150 SUN: much smaller than in conventional CPVs, resulting in high module cost. For the actual application of our module, we plan to increase the concentration ratio by shrinking the cell size.
2.2 Measurement of CPV characteristics
All the measurements of the CPV modules were carried out outdoors under sunlight in Kyoto, which is located at 34°44′N, 135°46′E. The CPV module was mounted on a home-made tracking system to track the sun. The photovoltaic characteristics of the modules were measured on different dates, and the measurement of each module was carried out on the same day. Since the intensity and spectrum of sunlight varies during the day, we can deduce the dependence of module’s photovoltaic characteristics on DNI. The I-V characteristics of the module were measured using an I-V curve tracer (EKO MP-160). DNI was measured using a pyrheliometer (EKO MS-56). The spectrum of the sunlight was measured using spectroradiometer (Opto Research MSR-7000N). The sensor of the spectroradiometer is at the base of a pipe through which only direct solar radiation can arrive at the sensor. The inner diameter and length of the pipe are 68 mm and 450 mm, respectively. The CPV module was attached to a temperature-control unit mounted on the tracking system. The temperature control unit maintains the module at a constant temperature during the taking of measurements. The control unit comprises an aluminum plate for heat dissipation (200 x 200 x 3 mm) and an aluminum block for cooling (50 x 50 x 10 mm) sandwiching Peltier devices (40 x 40 x 5 mm). The CPV module is attached, using thermal grease, to an aluminum block for cooling, and a thermocouple is attached at the center of the aluminum block for cooling beneath the module. The temperature measured by the thermocouple was defined as the module temperature. No bypass diode was connected to the CPV module.
2.3 Measurement of optical characteristics
The transmittance of the lens and the anti-reflective coating on the top face of the solar cell was measured using a spectral sensitivity characteristics measurement apparatus (Bunkoukeiki CEP-25RR) and a variable-angle spectroscopic ellipsometer (Woollam VASE), respectively. The transmittance of the lens was measured using the following method. The light exiting the beam splitter entered the top face of the lens. The light which exited the back face of the lens was fed into the integrating sphere, where its intensity was measured by a photodiode attached to the integrating sphere.
3. Results and discussion
3.1 DNI dependence of PV characteristics
Figures 3(a)-3(d) show the DNI dependence of the PV characteristics of two modules made using the same method. The module temperature was set at 25 °C. The short-circuit current (Isc) of modules A and B in Fig. 3(a) increased linearly with increasing DNI. Each data item from modules A and B can be roughly plotted on two lines with different slopes. We speculate that the data on the DNI dependence of FF in Fig. 3(d) can be plotted on two lines with different slopes, as shown in Fig. 3(d), and assume that the critical point of DNI at which the slope of the Isc line changes is close to the critical value for FF. The validity of our speculation is shown later. It should be noted that the energy conversion efficiency η in Fig. 3(c) has its maximum value around the critical DNI values of Isc and FF. No DNI dependence on open-circuit voltage (Voc) was observed in Fig. 3(b). The Voc distribution of the two modules is different. This is likely to be due to minor difference between the characteristics of each module.
Fig. 3 DNI dependence of PV characteristics. These Figures show the Isc, Voc, η and FF dependence of DNI. Blue dots: module A on 30 July 2014. Red dots: module B on 31 July 2014. The arrows indicate the critical point.
DNI varies with time over the day, since the optical path length of sunlight in air mass changes with the sun’s elevation angle and weather conditions. The light intensity of wavelengths from 400 - 665 nm, which are absorbed by the top cell, varies more with path length than that of wavelengths from 665 - 1350 nm, which are absorbed by the middle and bottom layers [8]. Thus, with increasing DNI, the intensity of the light absorbed by the top cell increases to a greater extent than that absorbed by the middle and bottom cells. The dependence of Isc on DNI in Fig. 3(a) shows that the slope of Isc below the critical DNI value is steeper than that above the critical value. Therefore, an increase in Isc with DNI under the critical value is likely to be caused by an increase in the top cell’s current, indicating that the CPV module is top-limited.
In the same way, the increase in Isc with DNI over the critical value is governed by the current in the middle or bottom cells, indicating that the module is middle or bottom limited. Since the PMMA refractive lens in the module absorbs incident sunlight at around 1160 nm, which generates photocurrent in the bottom cell, the current in the bottom cell should be smaller than that in the middle cell in DNI above the critical value. Thus, in this DNI range, the CPV module is bottom-limited. We speculate that the module is current-matched, in which the photocurrent of the top, middle and bottom cells is almost the same, around the critical value of DNI. It is known that the FF value of the 3-junction cell in current-matched is smaller than that in non-current-matched [9]. This fact supports our speculation that the FF value has a minimum value around the critical value of DNI for Isc, as shown in Figs. 3(a) and 3(c).
We calculated the spectrum-matching ratio (SMR) [10] at each critical value to analyze the measurement results from the viewpoint of the sunlight spectrum. The SMR can be expressed by Eq. (1) using the photocurrent of the top and bottom cell, since our CPV module was operated under top- or bottom-limited conditions for our measurements.
where is the photocurrent of the top and bottom cell, calculated using the quantum efficiency and the spectrum of the sunlight when data were obtained in Figs. 3; and is the photocurrent of the top and bottom cell calculated using the quantum efficiency and AM1.5D sunlight. The SMRs of module A and B at the critical value were closely similar at 1.14 and 1.19, respectively. This result suggests the rate of photocurrent in the top cell to that in bottom cell to be almost the same for module A and B at each critical value. Both SMRs were greater than 1, indicating that our CPV module is better current-matched under a blue-shifted spectrum than under the AM1.5D spectrum.Although modules A and B were assembled using the same method and employed the same type of solar cells on the same wafer, the critical DNI value of each module was different, as shown in Figs. 3. The ratio of photocurrent in the top cell to that in middle cell at the critical points in module A and B was calculated to be 1.02 and 1.00, respectively. These ratios are almost identical, meaning that the ratio of photons absorbed in the top, middle, and bottom cells of module A is almost the same as the ratios in module B, and demonstrating the relative intensity distribution of the sunlight spectrum of module A to be almost the same as that of module B. The critical value of modules A and B should therefore be the same if both modules are measured under the same sunlight spectrum and intensity.
A conversion efficiency of 37.1% was achieved in module B at a module temperature of 25 °C, as shown in Fig. 4(a). The measurement conditions were a DNI of 807 W/m2 and Air mass of 1.13. Figure 4(b) shows the sunlight spectrum when the conversion efficiency of 37.1% was obtained. SMR was 1.30 under this sunlight spectrum. The module was designed to maximize the irradiated area of sunlight absorbed by the top cell. The acceptance angle (the misaligned angel corresponding to a 10% drop of Isc) is ± 1.65°: although this value is large enough for our tracking system to track the sun, an optimal tradeoff between irradiation area and acceptance angle will be determined in the view of the total cost of the CPV system.
Fig. 4 (a) I-V characteristics of module B. Measurement was carried out on one solar cell in the CPV module whose temperature was maintained at 25 °C by a Peltier setup. (b) The sunlight spectrum was measured when the I-V characteristics were those seen in Fig. 4(a). These data were obtained in Kyoto at 13:42 on 31 July 2014.
Figure 5 shows the conversion efficiency of 25 cells in the CPV module B, measured on the same day. DNI varied during the measurements due to the changing angle of solar elevation. Although the DNI value where each cell was measured was different, the variation in conversion efficiency was within 2%.
Fig. 5 The variation of the conversion efficiency of 25 solar cells in the module B, measured on 29 September 2014. SMR was 0.93 - 1.01 during these measurements.
3.2 Analysis of optical loss in the CPV module
The PV characteristic of a CPV module is usually worse than that of solar cells that are not integrated into a module. The decrease in the PV characteristic is caused by various factors, such as optical loss of the incident sunlight by the parts comprising the module, higher series resistance due to inadequate electrical connections between the solar cells and the circuit board, spectrum changes in the incident sunlight, and non-uniform intensity of the sunlight on the solar cell. To elucidate the factors degraded the PV performance of the CPV module, we investigated the difference in PV characteristics between the CPV module and the bare solar cell before integration into the module. The PV characteristic of the bare cell was estimated using a flash test under the light source, in which the rate of the photocurrent in the top cell to the photocurrent in the middle cell was equal to when using AM1.5D. The conversion efficiency of the bare cell was 42.4% at Isc = 11 mA. The conversion efficiency of the CPV module was 35.5% at Isc = 10.3 mA under sunlight of SMR = 1.01, in which the rate of the photocurrent in the top cell to the photocurrent in the bottom cell is close to that for AM1.5D. The modularization loss is defined as 1-ηmodule/ηcell, where ηmodule and ηcell are the CPV module’s efficiency (35.5%) and the solar cell’s efficiency (42.4%), respectively. The modularization loss was 16.3%.
To investigate the factor of the modularization loss, we analyzed the optical loss of our module. Incident sunlight is lost mainly due to reflection from and absorption by the lens, and reflection from the anti-reflective coating on the top surface of the solar cell. The optical loss of the lens LA and the optical loss due to the anti-reflective coating on a solar cell LB can be expressed by Eqs. (2-3), respectively:
where P(λ), TA (λ), and TB (λ) are photon distribution at λ, transmittance of the lens, and transmittance of the anti-reflective coating of a solar cell, respectively. k is a subscript that specifies the wavelength range of the incident sunlight that is lost in the module, and n1 and n2 are the minimum and maximum wavelength in this range, respectively. k is expressed as “top,” “middle,” “bottom,” or “all,” corresponding to the wavelength range of the sunlight absorbed in the top, middle, bottom, and all the cells, respectively. The values for transmittance of the lens array and the anti-reflective coating of the solar cells shown in Fig. 6 were used for calculation using Eqs. (2-3).Fig. 6 The transmittance of the lens array and the anti-reflective coating of a solar cell. The black line shows the transmittance of the lens array. The red line shows the transmittance of the anti-reflective coating of a solar cell.
Total optical loss in the module for k is expressed by Eq. (4),
TA (λ) and TB (λ) were measured experimentally. Using TA (λ), TB (λ), and the spectrum P (λ) of AM1.5D, LA(k) and LB(k) is calculated from Eqs. (2-4), as shown in Table 1. The shadow loss due to the grid electrodes (about 2%) is not included in the optical loss.
Table 1. Optical loss calculated from transmittance of lens and AR layer on top surface of solar cell
The optical loss L(top), L(middle), and L(bottom) was 4.6%, 5.6%, and 16.5%, respectively. The optical loss L(bottom) is much greater than L(top) or L(middle). This is because the PMMA lens of our module absorbs incident sunlight at around 1160 nm that is absorbed in the bottom cell, while the lens is transparent to incident sunlight of 400 - 885 nm that is absorbed in the top and middle cell, except for a small absorption peak around 885 nm. There are reports simulating the optical loss of CPVs with secondary optics. In these reports, the optical loss of the primary lens is 10 - 13%, and the total optical loss of the primary lens and secondary optics is 14 - 20% [11–15]. The optical loss of the lens LA(all) in our CPV module was much smaller, at 7.6% (Table 1). It should be noted that the total optical loss L(all) of 9.6% seen in our module is also smaller than the reported value for optical loss of 14 - 20% that does not include LB(all). Optical loss arises at the interface between two materials with different refractive indexes. Our module has several interfaces inside the module, such as PMMA/adhesive/glass interfaces, and glass plate/adhesive/solar cell interfaces, as shown in Fig. 1(b). The variation in refractive indexes in the interfaces is within 0.11 in our module. On the other hand, CPVs with secondary optics have lens/air and secondary-optics/air interfaces inside the module, and the variation in refractive indexes in these interfaces is around 0.4 - 0.5. The small refractive index variations in our CPV module make it possible to achieve lower optical losses than with those seen in CPVs with secondary optics. Since our CPV has a low optical loss of 9.6%, the module has the potential to achieve a high conversion efficiency if the modularization loss can be minimized.
We considered the modularization loss that does not include the optical loss, which was 6.7%. This result indicates that the PV performance of the CPV module is degraded by other factors besides optical loss. We speculate that the main contributor to this loss is the non-uniformity of sunlight irradiation on the CPV module. Our module has no secondary optics, so the irradiation light on the cell in the module is not uniform, whereas in the flash test, the irradiated light on the bare cell is uniform. This non-uniform irradiation brings down the CPV module’s efficiency compared to the bare cell. The decrease in efficiency is not due to the non-uniform irradiation in the three subcells but to non-uniform irradiation of the surface of the top cell [7], which induces a higher photocurrent density in small areas in the cell. This photocurrent generates higher Joule losses than seen in a cell with uniform irradiation, since the resistance of the top cell’s surface is greater than in the other cells. Although in our previous study the Joule loss in the top cell was reduced by expanding the irradiated area of sunlight absorbed at the top cell, the results for modularization loss indicate that a simple reduction of Joule loss in the top cell is not sufficient to improve the cell’s efficiency. Optimization of the grid electrode design is needed to decrease the resistance between the top cell and the grid electrodes to minimize the Joule loss. Although Joule loss of 6.7% affects the FF value of the CPV module, the FF values of 0.83 - 0.85 for our CPV module, shown in Fig. 3(d), are comparable to those reported for conventional CPV modules with secondary optics [16–19].
In the flash test, the highest conversion efficiency of 43.5% was obtained at a concentration ratio of 400, greater than that in the CPV module. Although the sunlight distribution irradiated on the solar cell is different for the CPV module and the flash test, it is possible to increase the module’s efficiency by both decreasing the Joule loss in the top cell and raising the concentration ratio. Improvement of the concentration ratio and the optimization of solar cell size will be necessary to reduce the cost of the CPV module.
4. Conclusion
We have developed a compact and thin concentrating photovoltaic (CPV) module using solar cells sized less than 1 mm x 1 mm that are attached to the back of a lens array without secondary optics. In this study, we constructed a module in which the irradiated area of sunlight absorbed in the top cell is optimized. We measured its PV characteristics under various direct normal irradiances (DNIs) and sunlight spectra to find the maximum energy conversion efficiency. We demonstrated that our CPV module achieves an energy conversion efficiency of 37.1% under optimal measured conditions for sunlight intensity and spectrum. The modulation loss and the optical loss of our module were estimated to be 16.3% and 9.6%, respectively. The optical loss was smaller than that for conventional CPVs with secondary optics. The modularization loss that does not include the optical loss was 6.7%, which is mainly due to Joule loss in the top cell, induced by the non-uniform irradiation of the cell. Since our CPV module has a lower optical loss of 9.6%, our module has the potential to achieve high conversion efficiency by optimizing the grid electrode design on the top cell to decrease the Joule loss.
Acknowledgments
The authors would like to thank Mr. Michihiko Takase and Mr. Takeo Funaoka at AVC Networks Company, Panasonic Corporation for their continuing support and technical advice.
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